It is argued that deep atmospheric convection might occur during winter in ice-free high-latitude oceans, and that the surface radiative warming effects of the clouds and water vapor associated with this winter convection could keep high-latitude oceans ice-free through polar night. In such an ice-free high-latitude ocean the annual-mean SST would be much higher and the seasonal cycle would be dramatically reduced - making potential implications for equable climates manifest. The constraints that atmospheric heat transport, ocean heat transport, and CO2 concentration place on this mechanism are established. These ideas are investigated using the NCAR column model, which has state-of-the-art atmospheric physics parameterizations, high vertical resolution, a full seasonal cycle, a thermodynamic sea ice model, and a mixed layer ocean.